## An integral that counts the zeros of a function

Hungerbühler, Norbert (Department of Mathematics, ETH Zürich, Zürich, Switzerland) ; Wasem, Micha (School of Engineering and Architecture (HEIA-FR), HES-SO // University of Applied Sciences Western Switzerland)

Given a real function f on an interval [a, b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f , f’ and f’’. In particular, by approximating the integral with the trapezoidal rule on a fine enough grid, we can compute the number of zeros of f by evaluating finitely many values of f , f’ and f’’. A variant of the integral even allows to determine the number of the zeros broken down by their multiplicity.

Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEIA-FR
Institute:
Aucun institut
Subject(s):
Ingénierie
Date:
2018-12
Pagination:
13 p.
Published in:
Open Mathematics
Numeration (vol. no.):
2018, vol. 16, no. 1
DOI:
ISSN:
2391-5455
Appears in Collection:

Fulltext:

PDF

Rate this document:

1
2
3

(Not yet reviewed)